A search plane carries radar equipment that can detect metal objects (like submarine periscopes or plane wreckage) on the ocean surface up to 15.5 miles away. If the plane completes a circular flight pattern of 471 miles in circumference, how much area will it search?

Answers

Answer 1

The area that the considered search plane searches with the given figures is 16957.42 miles² approximately.

How to find the area of a circle?

Suppose the circle has radius of 'r' units, then, its area is given as:

[tex]A = \pi \times r^2[/tex] sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:

[tex]\pi \times (\dfrac{d}{2})^2[/tex] sq. units

How are radius and circumference of a circle related?

Suppose that a considered circle has:

Circumference = C unitsRadius = r units

Then, we get:

[tex]C = 2\pi r \: \rm units[/tex]

So, the radar scans the surface of ocean in a circular area with radius of 15.5 miles.

That circular area is itself moved in a circular path (due to circular motion of the plane with 471 miles circumference of the circular path).

The graph given describes the region of scan.

The blue region's area = Outer circle's area - Internal circle's area

The Internal circle has circumference 471 miles, let its radius be 'r' miles, then:

[tex]471 = 2\pi r\\\\r = \dfrac{471}{2\pi} \: \rm miles[/tex]

The outer circle has the radius = internal circle's radius + diameter of the radar circle =  [tex]\dfrac{471}{2\pi} + 2(15.5) =\dfrac{471}{2\pi} + 30 \: \rm miles[/tex]

Thus, we get:

Area of internal circle = [tex]\pi r^2 = \pi \times \left( \dfrac{471}{2\pi} \right)^2 \approx 17,653.56 \: \rm miles ^2[/tex]Area of outer circle = [tex]\pi \times \left( \dfrac{471}{2\pi} + 30 \right )^2 \approx 34610.98 \: \rm miles ^2[/tex]

Net area which is searched by the search plane ≈ 34610.98 - 17653.56 miles²

Net area which is searched by the search plane ≈ 16957.42 miles²

Thus, the area that the considered search plane searches with the given figures is 16957.42 miles² approximately.

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A Search Plane Carries Radar Equipment That Can Detect Metal Objects (like Submarine Periscopes Or Plane

Related Questions

Can U Guys Tell Me The Angle And Type?

Answers

Answer:

The angle is 90°, and the type of angle is a right angle.

Step-by-step explanation:

That is a right angle, the little box and the straight lines indicate that is one. A right angle will always be 90°.

Question 2 of 21
In Accra, 30% of workers owns a car. In a sample of 10 workers, what is the probability that exactly three workers owns a car?
O A. 0.267
OB. 0.65
O C. 0.48
O D.0.73

Answers

Using the binomial distribution, it is found that the probability that exactly three workers owns a car is given by:

A. 0.267.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

In this problem:

30% of workers owns a car, hence p = 0.3.A sample of 10 workers is taken, hence n = 10.

The probability that exactly three workers owns a car is given by P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.267[/tex]

Hence option A is correct.

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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS IF YOU DO THEN YOU GET REPORTED AND PLEASE EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

Angle A=60

Step-by-step explanation:

If ABC is approximately equal to DEF, A=D.

So x+30=2x

x+30=2x -> 30=x

If A=x+30 and x=30 then 30+30=60.

The following chart shows a company's sales records of four employees over the past year,
Sales by Month
50
45
40
Sales 61000)
35
Ben
Marcel
30
25
Rebecca
20
2
8 9 10 11 12
Month
Based on this graph, which employee is likely to have the greatest sales next month?
a Ben
b Marcel
c Kim
d. Rebecca
Save and Exit
Next
Sul
Mark this and return

Answers

Answer:

The answer is C

Step-by-step explanation:

Please help me answer this

Answers

Answer:

option A is the correct answer

Solve the equation for x.
X-7 = 7
Enter the number that belongs in the green box.
x = [?]

Answers

Answer:

14

Step-by-step explanation:

1. Add 7 to both sides

2. This leaves us with x=14


Which of the following ordered pairs is represented by a point located on the x-axis?
(-3, -3)
( - 6,6)
(5,0)
(0,5)

Answers

Answer:

(5,0)

Step-by-step explanation:

The # 5 is on the x axis and there is no value for the y since it is 0. This means that this ordered pair will be located on the x-axis.

a rectangular prism has length x, width x/2 and height x/3. Which expression represents the volume of the prism?

Answers

Answer:

x^3 / 6

Step-by-step explanation:

Multiply the three dimensions to get the volume

x * x/2 * x/3 =  

The expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

It is given that, the length is x, width x/2, and height is x/3.

The volume of the rectangular prism is the product of the length, width, and height.

V= length × width × height

V=x × x/2 × x/3

Apply the multiplication operation in the fraction

Simply multiply the numerators to obtain the product's numerator and the denominators to obtain the product's denominator in order to multiply two fractions.

V=x³/6

Thus, the expression represents the volume of the prism that will be, x³/6. The expression is obtained by finding the volume of the rectangular prism for the given data.

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The distance between second base and third base on a regulation baseball field is 30 yards. Choose the word and number to complete the sentence correctly. To convert 30 yards to feet

Answers

Answer:

To convert 30 yards to feet, multiply by 3.

Step-by-step explanation:

We have to find out how many feet is in 1 yard and we have to multiply by 3 to find the answer. So the answer is multiply by 3

NO LINKS!!!
Movies generally lose 23% of it's audience for each week in the theatre. A movie STARTED with an audience of 196 people per viewing.



Answers

Answers:

a) The equation is [tex]y = 196(0.77)^x[/tex]

b) See image attachment below

c) See image attachment below

d) Week 10

=======================================================

Explanation:

a)

One common template for an exponential equation is [tex]y = a*b^x[/tex] where 'a' is the starting amount and b is the growth or decay factor.

a = 196 is the starting amount of people who saw the movie per showtime

b = 1-0.23 = 0.77 is the decay factor. If the view count goes down by 23%, then we keep the remaining 77%

Therefore we go from [tex]y = a*b^x[/tex] to [tex]y = 196(0.77)^x[/tex]

x = number of weeks

y = number of people, per viewing, who saw the movie for the particular week

--------------------

b)

Plug in x = 0 to find that y = 196

Plug in x = 1 to get y = 150.92 which rounds to y = 151 since we're talking about the number of people

Repeat for x = 2 all the way up to x = 9 to account for the first ten weeks. We stop at 9 instead of 10 because we started at x = 0.

The table is shown in the attachment below next to the graph.

I'm not sure why your teacher put a dollar sign over the second column of the table when it should be the number of people. It might be a typo. If they meant to do it, then there's missing information about ticket prices.

--------------------

c)

The graph is shown below. You can plot each (x,y) point on the same grid and then draw a curve through them. A much quicker way is to use software like GeoGebra (which is what I used) or Desmos or a pocket calculator. There are tons of many options to pick from. Feel free to choose your favorite.

The blue dashed segments on the graph visually help verify the result of part (d). We have y = 20 lead to an x value somewhere between x = 8 and x = 9. When submitting the graph to your teacher, you'll leave out the blue dashed segments.

--------------------

d)

Refer to the table we made in part (b). We have x = 9 lead to y = 19 approximately which is when y is below 20 people. Recall that x = 0 refers to week 1, so x = 9 refers to week 9+1 = 10. Week ten is where the view count drops below 20 people per showing.

If you wanted to use the graph in part (c), then you'd follow the blue dashed line mentioned earlier. Start at the y axis at y = 20. Trace the blue dashed line until reaching the curve. Then drop straight down to arrive somewhere between x = 8 and x = 9. Round up to x = 9. Then make the adjustment to go from x = 9 to week ten.

If you want an algebraic method, then follow the steps below.

Plug in y = 20 and solve for x. We'll need to involve logarithms to isolate the exponent.

[tex]y = 196(0.77)^x\\\\20 = 196(0.77)^x\\\\20/196 = (0.77)^x\\\\0.1020408 \approx (0.77)^x\\\\(0.77)^x \approx 0.1020408\\\\\text{Log}\left((0.77)^x\right) \approx \text{Log}(0.1020408) \\\\x*\text{Log}\left(0.77\right) \approx \text{Log}(0.1020408) \\\\x \approx \text{Log}(0.1020408)/\text{Log}\left(0.77\right) \\\\x \approx 8.7325564 \\\\[/tex]

This rounds up to x = 9 leading to week ten as the answer.

As confirmation

[tex]y = 196(0.77)^x = 196(0.77)^8 \approx 24.22 \approx 24\\\\y = 196(0.77)^x = 196(0.77)^9 \approx 18.65 \approx 19\\\\[/tex]

Answer:

Part (a)

We can model this as an exponential equation.

General form of an exponential equation: [tex]y=ab^x[/tex]

where:

a is the initial valueb is growth factorx is the independent variabley is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

As the movie theatre lost 23% of its audience each week, the growth (decay) factor will be 100% - 23% = 77%  →  0.77

Given:

a = 196b = 0.77x = times (in weeks)y = audience (in number of people)

Substitute the given values into the formula to create the exponential equation:

[tex]y=196(0.77)^x[/tex]

Part (b)

[tex]\begin{tabular}{| c | r |}\cline{1-2} \bf weeks & \bf audience \\\cline{1-2} 1 & 150.92\\\cline{1-2} 2 & 116.21\\\cline{1-2} 3 & 89.48\\\cline{1-2} 4 & 68.90\\\cline{1-2} 5 & 53.05\\\cline{1-2} 6 & 40.85\\\cline{1-2} 7 & 31.46\\\cline{1-2} 8 & 24.22\\\cline{1-2} 9 & 18.65\\\cline{1-2} 10 & 14.36\\\cline{1-2}\end{tabular}[/tex]

**all values rounded to 2 dp**

Part (c)

see attached for graph

Part (d)

Set y < 20 and solve for x:

[tex]\begin{aligned}196(0.77)^x & < 20\\\\(0.77)^x & < \dfrac{5}{40}\\\\\ln (0.77)^x & < \ln\left(\dfrac{5}{49}\right)\\\\x\ln (0.77) & < \ln\left(\dfrac{5}{49}\right)\\\\x & > \dfrac{\ln\left(\dfrac{5}{49}\right)}{\ln (0.77)}\\\\x & > 8.732555795\end{aligned}[/tex]

Therefore, the movie audience will fall below 20 people per viewing during the 9th week.

There are 165 concrete blocks available to make a retaining wall. The bottom 3
rows will all have the same number of blocks. The next six rows will each have 2
blocks fewer than the row below it. How many blocks are in each row?

Answers

Answer:

12

Step-by-step explanation:

The number of blocks in each row, from bottom to top, is: 23, 23, 23, 21, 19, 17, 15, 13, 11.

Step 1: Let's assume the number of blocks in each row of the bottom 3 rows is "x."

Step 2: The next six rows will each have 2 blocks fewer than the row below it. So, the number of blocks in each of these rows can be represented as:

x - 2, x - 4, x - 6, x - 8, x - 10, x - 12.

Step 3: Now, we can calculate the total number of blocks in all the rows.

For the bottom 3 rows, there are a total of 3 * x = 3x blocks.

For the next six rows, there are a total of (x - 2) + (x - 4) + (x - 6) + (x - 8) + (x - 10) + (x - 12) = 6x - 42 blocks.

Step 4: The total number of blocks in the wall is given as 165 blocks. So, we can set up an equation:

3x + 6x - 42 = 165

Step 5: Now, solve for x:

9x - 42 = 165

9x = 165 + 42

9x = 207

x = 207 / 9

x = 23

Step 6: Now that we have the value of x, we can find the number of blocks in each row:

The bottom 3 rows: x = 23 blocks each.

The next six rows:

x - 2 = 23 - 2

       = 21 blocks,

x - 4 = 23 - 4

       = 19 blocks,

x - 6 = 23 - 6

       = 17 blocks,

x - 8 = 23 - 8

        = 15 blocks,

x - 10 = 23 - 10

         = 13 blocks,

x - 12 = 23 - 12

         = 11 blocks.

So, the number of blocks in each row, from bottom to top, is: 23, 23, 23, 21, 19, 17, 15, 13, 11.

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Its a multiple choice, HELP IM BEGGING​

Answers

Answer:

B)

E)

Step-by-step explanation:

       translation                                   Dilation

M(x,y) ——————>M”(x”,y”)=(x+5,y+8) ——————> M’(x’,y’)=(3x”,3y”)

S(-5,-8) ——————>S”(x”,y”)=(0,0) ——————> S’(x’,y’)=(0,0)

R(-7,-6) ——————>R”(x”,y”)=(-2,2) ——————> R’(x’,y’)=(-6,6)

Q(-8,-10) ——————>Q”(x”,y”)=(-3,-2) ——————> Q’(x’,y’)=(-9,-6)

How much sugar is in 200 grams of 5% sugar syrup

Answers

Answer:

10 grams

Step-by-step explanation:

200 x 5 = 1000

If we move the decimal over two places left we get :

10.00

That means that there are 10 grams of sugar in 200 grams of 5% sugar syrup

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Have a nice day.

A $299.99 grill was discounted 25% for a labor day sale. When the sale ended, the sale price increased 25%. How much is the grill now?

Answers

299.99 - 25% = 274.99 274.99 + 25% = 299.99

If you roll a 6-sided die 54 times, what is the best prediction possible for the number of times
you will roll a five?

Answers

50% of the time (27 times) you will get an even number

Help Me on this!!


[tex] \\ \\ [/tex]

Answers

So here we are given that a || b and c || d, so the quadrilateral formed by the intersection of the four lines is just a parallelogram, so recall the property of parallelogram that parallelogram's opposite angles are always equal and the interior angles on the same side add up to 180°, and the property of angles that the alternate angles are always equal (that's angles Like in the Shape Z) and vertically opposite angles are equal (like in shape of X) and the property of linear pair i.e the sum of all angles on a plane line is 180°.

Now, as angles 3 and 7 are on a line d, so their sum will just be 180°, by property of linear pair

[tex]{:\implies \quad \sf m\angle 3+m\angle 7=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 7+74^{\circ}=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 7=180^{\circ}-74^{\circ}}[/tex]

[tex]{:\implies \quad \boxed{\bf{m\angle 7=106^{\circ}}}}[/tex]

Also, as angles 8 and 3 are vertically opposite angles, so they will be same, so we have

[tex]{:\implies \quad \boxed{\bf{m\angle 8=74^{\circ}}}}[/tex]

Now also, angle 7 and angle 11 are opposite angles of the parallelogram, so they will be equal, so we have :

[tex]{:\implies \quad \boxed{\bf{m\angle 11=106^{\circ}}}}[/tex]

Also, the interior angles on same side of Parallelogram add upto 180°, so we can have ;

[tex]{:\implies \quad \sf m\angle 11+m\angle 13=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 13+106^{\circ}=180^{\circ}}[/tex]

[tex]{:\implies \quad \sf m\angle 13=180^{\circ}-106^{\circ}}[/tex]

[tex]{:\implies \quad \boxed{\bf{m\angle 13=74^{\circ}}}}[/tex]

Also, Opposite angles of Parallelogram are equal, so angle 6 will be equal to angle 13, so angle 6 will be 74° and we also know the Vertically Opposite angles are equal. So, for angle 1 we have

[tex]{:\implies \quad \boxed{\bf{m\angle 1=74^{\circ}}}}[/tex]

Now, we are end with the conclusion :

[tex]{\bf{m\angle 1=74^{\circ}}}[/tex][tex]{\bf{m\angle 7=106^{\circ}}}[/tex][tex]{\bf{m\angle 8=74^{\circ}}}[/tex][tex]{\bf{m\angle 11=106^{\circ}}}[/tex][tex]{\bf{m\angle 13=74^{\circ}}}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Measure of Angle 3 is given, that is : Angle 3 = 74°

And the lines a and b are parallel, similarly line c and d are parallel to each other as well.

Now, let's just use property of angles on parallel lines to find measure of each angle we have been asked.

[tex]\qquad \tt \dashrightarrow \: \angle1 = \angle3 = 74 \degree[/tex]

[ By Corresponding Angle pair ]

・ .━━━━━━━†━━━━━━━━━.・

[tex]\qquad \tt \dashrightarrow \: \angle7 + \angle3 = 180 \degree[/tex]

[ By Linear Pair ]

[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - \angle3 [/tex]

[tex]\qquad \tt \dashrightarrow \: \angle7 = 180 - 74[/tex]

[tex]\qquad \tt \dashrightarrow \: \angle7 = 106 \degree[/tex]

・ .━━━━━━━†━━━━━━━━━.・

[tex]\qquad \tt \dashrightarrow \: \angle8 = \angle3 = 74 \degree[/tex]

[ By Vertical opposite angle pair ]

・ .━━━━━━━†━━━━━━━━━.・

[tex]\qquad \tt \dashrightarrow \: \angle7 = \angle11 = 106 \degree[/tex]

[ opposite angles of a Parallelogram ]

・ .━━━━━━━†━━━━━━━━━.・

[tex]\qquad \tt \dashrightarrow \: \angle13= \angle3 = 74 \degree[/tex]

[ by Corresponding Angle pair ]

How do the charges compare when two objects are charged through friction? The objects become oppositely charged and have equal amounts of charge. The objects become positively charged and have equal amounts of charge. The objects become negatively charged and have different amounts of charge. The objects become oppositely charged and have different amounts of charge.

Answers

Answer:

If both objects started with no charge, they would carry opposite charges of the same magnitude after rubbing.

Step-by-step explanation:

When one insulator is rubbed against another, some electrons on one insulator might travel to the surface of the other insulator. Electrons are neither lost nor created in this process- they are just moved from one surface to the other.

Let the two insulators in this question be denoted as [tex]A[/tex] and [tex]B[/tex]. Assume that both insulators were initially not charged.

Let [tex]{\rm e}[/tex] denote the fundamental charge. Each electron carries a negative charge of [tex](-1\; {\rm e})[/tex]. Assume that [tex]n[/tex] electrons are moved from insulator [tex]A\![/tex] to insulator [tex]B\![/tex]:

Insulator [tex]A\!\![/tex] would now have [tex]n\![/tex] fewer electrons than it used to do. Thus, the charge on insulator [tex]A\![/tex] would have been reduced by [tex]n \times (-1\; {\rm e})[/tex]. Since insulator [tex]A[/tex] started with no charge, it would now carry a charge of [tex]0 - n \times (-1 \; {\rm e}) = n\; {\rm e}[/tex].Insulator [tex]B[/tex] would now have [tex]n[/tex] more electrons than it used to do. The charge on insulator [tex]B\![/tex] would have increased by [tex]n \times (-1\; {\rm e})[/tex]. Since insulator [tex]B[/tex] started with no charge, it would now carry a charge of [tex]0 + n\times (-1\; {\rm e}) = (-n\; {\rm e})[/tex].

In other words, the insulator that lost some electrons (which are negatively charged) now carries less negative charge and becomes positively charged. In contrast, the insulator that gained some electrons now carries more negatively charge becomes negatively charged.

The amount of electrons on the two objects combined stays unchanged. Thus, the amount of charge one insulator lost is equal to what the other insulator gained. Therefore, the sign of the charge on the two insulators would be different, but the magnitude (absolute value) of the charge would be equal.

Therefore, the two objects would be oppositely charged, with the magnitude of the charge on them being equal.

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

Step-by-step explanation:

the median is 26.5, but rounding that up the median will be 27. you can find this by determining the middle number of the data set.

12 times a number, x, minus 5 is ninety-one

Answers

Answer:

x=8

Solution:First, multiply 12 times x, like so:12xNow, subtract 5:12x-5This expression is equivalent to 91:12x-5=91Now, add 5 to both sides:12x=91+512x+96x=8

Hope it helps.

Do comment if you have any query.

[tex]12x-5 = 91\\\\\implies 12x = 91+5\\\\\implies 12x = 96 \\\\\implies x= \dfrac{96}{12}\\\\\implies x = 8[/tex]

Consider the line – 2x - 5y= 2.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:

Answers

Answer:

Step-by-step explanation:

A solid box with height 90cm, width 70cm and length 90cm needs to be painted.
The paint costs £0.02 per cm2.
How much will it cost to paint the outside of the box?

Answers

Answer:

£828

Step-by-step explanation:

The first step to solve this problem is to find the surface area of the solid box. The formula for surface area for a rectangular prism is [tex]2(wl+hl+hw)[/tex]where w is width, l is length, and h is height. Plugging values in gives [tex]2(90*90+70*90+70*90)=41400[/tex] cm^2.

Because each cm^2 of paint costs £0.02, a ratio can be created.

[tex]\frac{1}{0.02} =\frac{41400}{x}[/tex]

Cross multiplying gives: [tex]x=828[/tex], so to paint the whole outside of the box, it would cost £828.

Pls help easy math 2 pics

Answers

Answer:

in the problem 17 the answer is 30 becase you times 6 and 6 and you git 30.problem 18 you do the same thing

Step-by-step explanation:

hope this helps if not let me now

solve for x :)
i’m not sure how to solve this it’s from geometry lesson 10.2

Answers

Step-by-step explanation:

Angle of a circle = 360

x + 90 + 84 + 16 = 360

x + 190 = 360

x = 170°

HELP PLEASEEEEEEEEEEEe

Answers

Answer:X + (2 and 1/2) - 3/4 = 5 and 1/4

X + 2 and 2/4 - 3/4 = 5 and 1/4 <--- common denominator

X + 10/4 - 3/4 = 21/4

X + 7/4 = 21/4

X = 21/4 - 7/4 = 14/4 = 7/2 = 3 and 1/2


One angle of a rhombus measures 110, and the shorter diagonal is 4 inches long. How long is the side of the rhombus?

Answers

side of rhombus: 2.44 inch

Use the sine rule:

[tex]\sf \dfrac{sin(A)}{a} = \dfrac{sin(B)}{b}[/tex]

=============                       Let the side be "b"

[tex]\rightarrow \sf \dfrac{sin(110)}{4} = \dfrac{sin(35)}{b}[/tex]

[tex]\rightarrow \sf b = \dfrac{sin(35)*4}{sin(110)}[/tex]

[tex]\rightarrow \sf b = 2.441549178[/tex]

[tex]\rightarrow \sf b =2.44 \ in[/tex]

Answer:

3.5 in (nearest tenth)

Step-by-step explanation:

Properties of a rhombus:

Quadrilateral (four sides & four interior angles)Parallelogram (opposite sides are parallel)All sides are equal in lengthOpposite angles are equal in measureDiagonals bisect each other at right anglesInterior angles sum to 360°Adjacent angles are supplementary (sum to 180°)Diagonals bisect interior angles

Therefore, a rhombus is made up of 4 congruent right triangles.

** see attached diagram **

To find the side length of the rhombus, we need to calculate the hypotenuse of the right triangle.

As the shorter diagonal is 4 in, the base of the right triangle is 2 in

The angles that measure 110° are the angles by the shorter diagonal.  Therefore, the base angle of the right triangle is 55°

Using cos trig ratio:

[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]

where:

[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse

Given:

[tex]\theta[/tex] = 55°A = 2H = x

[tex]\implies \sf \cos(55^{\circ})=\dfrac{2}{x}[/tex]

[tex]\implies \sf x=\dfrac{2}{\cos(55^{\circ})}[/tex]

[tex]\implies \sf x=3.486893591...[/tex]

Therefore, the side of the rhombus is 3.5 in (nearest tenth)

A bag has 1 red marble, 4 orange marbles, 2 green marbles, 6 blue
4
marbles, and 5 black marbles. You randomly pull a marble from the
bag, put it back, and then pull out another one.
What is the probability of not getting a black and then not getting a
green? Write your answer as a fraction.

Answers

Step-by-step explanation:

so first you must calculate the total amount of marbles there are, that being addition : 1+4+2+6+4+5 = 24 in total. now you want to make that into a fraction, 24/24 marbles, once again all together, so the probability of not getting a black marble is 5/24 and probability of not getting a green is 2/24.

order of operation 3×5+4×2-3​

Answers

[tex]3\times 5 +4 \times 2- 3\\\\=15+8-3\\\\=12+8\\\\=20[/tex]

100 POINTS!!! Please help ^^ it’s urgent!!

Answers

Answer:

x=1 y=4

Step-by-step explanation:

5x+y=9

10x-7y=-18

-35x-7y=-63

-45x=-45

x=1

y=4

(10)-(28)=18

Brainliest would be appreciated

Answer:

x=1 y=4

Step-by-step explanation:

a

Please help me outttt​

Answers

Answer:

2 + [tex]\sqrt{3}[/tex]

Step-by-step explanation:

In decimal form, it is also 3.73205080...

hope this helps :)

Find the area of the shaded region

Answers

Answer:

20.52 cm²

Step-by-step explanation:

[tex]\textsf{Area of a semicircle}=\sf \dfrac12\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\textsf{Area of a triangle}=\sf \dfrac12bh \quad \textsf{(where b is the base and h is the height)}[/tex]

Given:

[tex]\pi[/tex] = 3.14r = 6 cmb = 12 cmh = 6 cm

[tex]\begin{aligned}\implies \textsf{Shaded area} & =\sf \dfrac12\pi r^2-\sf \dfrac12bh\\ & = \sf \dfrac12 \cdot 3.14 \cdot 6^2-\dfrac12 \cdot 12 \cdot 6\\ & = \sf 56.52-36\\ ^& = \sf 20.52\:\:cm^2\end{aligned}[/tex]

Answer:

20.52cm^2

Step-by-step explanation:

from the picutre we can see that this is a semicircle with 2 right angle triangles inside it. to find the area we will solve for the semi circle then solve for the triangles and and subtract

circle area is [tex]\pi r^{2}[/tex] leaving the semicircle to be [tex]\frac{\pi r^{2} }{2}[/tex] for the semi circle

next we need the radius. since the diameter is given, we can solve for r by dividing it in two

12 ÷ 2 = 6

so the area of the semi circle is [tex]\frac{\pi 6^{2} }{2}[/tex]

this gives 18[tex]\pi[/tex]cm^2 if we simplify

next the triangles, since they are equal in size we can treat them as a square and stack them. this is because they have equal side lengths so when stacked they form a square:

base x height divided by 2 times 2 would be the normal process to find two equal triangles but you can see the division and multiplication cancel out

6x6= 36cm^2

finally subtracting the areas to find the shaded region and use 3.14 as pi

18[tex]\pi[/tex]cm^2 - 36cm^2 = 20.52cm^2

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